The value of limx→0x2sin1x is

For x≠0, we know that −1≤sin1x≤1Therefore −x2≤x2sin1x≤x2. But limx→0(−x2)=0=limx→0x2Hence, limx→0x2sin1x=0

The value of limx→0x2sin1x is

For x≠0, we know that −1≤sin1x≤1Therefore −x2≤x2sin1x≤x2. But limx→0(−x2)=0=limx→0x2Hence, limx→0x2sin1x=0

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The value of $\lim_{x \to 0} x^{2} \sin \frac{1}{x}$ is

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For $x \neq 0$ , we know that $- 1 \leq \sin \frac{1}{x} \leq 1$

Therefore $- x^{2} \leq x^{2} \sin \frac{1}{x} \leq x^{2}$ . But $\lim_{x \to 0} (- x^{2}) = 0 = \lim_{x \to 0} x^{2}$

Hence, $\lim_{x \to 0} x^{2} \sin \frac{1}{x} = 0$

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The value of limx→0x2sin1x is

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The value of $\lim_{x \to 0} x^{2} \sin \frac{1}{x}$ is